Harmonic oscillator eigenfunction
= Harmonic oscillator eigenfunction
{title2=$\psi_n$}
With oscillator length $\ell=\sqrt{\hbar/(m\omega)}$, the eigenfunctions are proportional to $H_n(x/\ell)e^{-x^2/(2\ell^2)}$. They have $n$ real nodes, <parity> $(-1)^n$, and energy $\hbar\omega(n+1/2)$.